1. Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis
- Author
-
Zhao, Mingyang, Jiang, Jingen, Ma, Lei, Xin, Shiqing, Meng, Gaofeng, and Yan, Dong-Ming
- Subjects
Computer Science - Computer Vision and Pattern Recognition ,Computer Science - Artificial Intelligence - Abstract
This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an $\ell_1$-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nystr\"om method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with substantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration., Comment: [CVPR 2024 Highlight] Project and code at: https://github.com/zikai1/CVPR24_PointSetReg
- Published
- 2024